Problem 63
Question
Find each absolute value. $$|-58|$$
Step-by-Step Solution
Verified Answer
58
1Step 1: Understand Absolute Value Definition
The absolute value of a number is its distance from zero on the number line regardless of direction. It is always non-negative.
2Step 2: Identify the Number Inside the Absolute Value
The number in question is (-58).
3Step 3: Apply the Absolute Value
Since absolute value measures distance and ignores direction, the absolute value of (-58) is simply 58.
Key Concepts
Distance from ZeroNon-NegativeNumber Line
Distance from Zero
Understanding the distance from zero is key to mastering absolute values. Absolute value measures how far a number is from zero on a number line.
Distance is always a positive measure because it considers only the magnitude, not direction. For instance, the distance from -58 to 0 is 58, and the distance from 58 to 0 is also 58.
This helps to explain why the absolute value of -58 is 58. It's about how far a number is from zero, not about whether it's on the left or right side of zero.
Distance is always a positive measure because it considers only the magnitude, not direction. For instance, the distance from -58 to 0 is 58, and the distance from 58 to 0 is also 58.
This helps to explain why the absolute value of -58 is 58. It's about how far a number is from zero, not about whether it's on the left or right side of zero.
Non-Negative
The term 'non-negative' can be confusing, but it simply means 'not negative.' All absolute values are non-negative.
When we calculate the absolute value, we only care about the distance, which ensures that the result can never be negative.
Consider the number line example again. Whether dealing with positive numbers (like 58) or negative numbers (like -58), the absolute value is the distance from zero, which is always a positive number or zero.
So, you can confidently say that \(|-58| = 58\), and it's non-negative.
When we calculate the absolute value, we only care about the distance, which ensures that the result can never be negative.
Consider the number line example again. Whether dealing with positive numbers (like 58) or negative numbers (like -58), the absolute value is the distance from zero, which is always a positive number or zero.
So, you can confidently say that \(|-58| = 58\), and it's non-negative.
Number Line
A number line is an essential tool for visualizing absolute value. Imagine a line with zero in the center. Positive numbers are to the right, and negative numbers are to the left.
To find the absolute value, you start at zero and measure how many steps it takes to reach the given number. You don't worry about the direction.
For example, to find \(|-58|\) on the number line, count 58 steps from zero towards -58.
Since we're only interested in the distance, \(|-58|\) equals 58, ignoring the direction entirely.
Practicing with a number line can make understanding absolute value much simpler.
To find the absolute value, you start at zero and measure how many steps it takes to reach the given number. You don't worry about the direction.
For example, to find \(|-58|\) on the number line, count 58 steps from zero towards -58.
Since we're only interested in the distance, \(|-58|\) equals 58, ignoring the direction entirely.
Practicing with a number line can make understanding absolute value much simpler.
Other exercises in this chapter
Problem 62
Multiply. $$ (2+a+b) 6 $$
View solution Problem 63
Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{13.4-5|1.2+4.6|}{(9.3-5.4)^{2}} $$
View solution Problem 63
Subtract. $$ 5-(-12) $$
View solution Problem 63
Divide, if possible, and check. If a quotient is undefined, state this. $$ \frac{28}{0} $$
View solution